Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
8001	2^338531+61313	101908	Stefano Morozzi	04/2022
8002	2^338531-9277	101908	Stefano Morozzi	04/2022
8003	2^338528-92727	101908	Stefano Morozzi	02/2023
8004	2^338527+191205	101907	Stefano Morozzi	06/2022
8005	2^338525+99621	101907	Stefano Morozzi	02/2023
8006	2^338524+54421	101906	Stefano Morozzi	01/2022
8007	2^338522-155811	101906	Stefano Morozzi	02/2022
8008	2^338523-16291	101906	Stefano Morozzi	01/2023
8009	2^338522-142137	101906	Stefano Morozzi	02/2023
8010	2^338521+183131	101905	Stefano Morozzi	02/2022
8011	2^338520+34945	101905	Stefano Morozzi	03/2022
8012	2^338518-182885	101905	Stefano Morozzi	04/2022
8013	2^338518+114633	101905	Stefano Morozzi	05/2022
8014	2^338518-12621	101905	Stefano Morozzi	12/2022
8015	2^338518-187325	101905	Stefano Morozzi	12/2022
8023	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
8016	2^338517-125955	101904	Stefano Morozzi	12/2021
8017	2^338517+126437	101904	Stefano Morozzi	12/2021
8018	2^338517-53499	101904	Stefano Morozzi	01/2022
8019	2^338515+30369	101904	Stefano Morozzi	01/2022
8020	2^338517-184623	101904	Stefano Morozzi	04/2022
8021	2^338515+89333	101904	Stefano Morozzi	05/2022
8022	2^338515+198813	101904	Stefano Morozzi	02/2023
8026	24502^14419+14419^24502	101903	Hans Havermann	01/2019
8024	2^338512-827	101903	Stefano Morozzi	12/2021
8025	2^338514-6611	101903	Stefano Morozzi	03/2022
8027	2^338509+5139	101902	Stefano Morozzi	01/2022
8028	2^338509+40205	101902	Stefano Morozzi	06/2022
8029	2^338511+19959	101902	Stefano Morozzi	09/2022
8030	2^338510-37877	101902	Stefano Morozzi	12/2022
8031	2^338507-188655	101901	Stefano Morozzi	12/2022
8032	2^338507-114457	101901	Stefano Morozzi	01/2023
8033	2^338504-152615	101900	Stefano Morozzi	01/2022
8034	2^338502-4587	101900	Stefano Morozzi	02/2022
8035	2^338502-166275	101900	Stefano Morozzi	01/2023
8036	2^338500-26865	101899	Stefano Morozzi	12/2021
8037	2^338501-177471	101899	Stefano Morozzi	12/2021
8038	2^338499-3915	101899	Stefano Morozzi	01/2022
8039	2^338501+32051	101899	Stefano Morozzi	02/2022
8040	2^338499+183533	101899	Stefano Morozzi	03/2022
8041	2^338500+35625	101899	Stefano Morozzi	03/2022
8042	2^338499+87579	101899	Stefano Morozzi	04/2022
8043	2^338498-117683	101899	Stefano Morozzi	02/2023
8046	2^338497-17041	101898	Enzo Doria	05/2013
8044	2^338497+150405	101898	Stefano Morozzi	11/2021
8045	2^338495+100533	101898	Stefano Morozzi	12/2021
8047	2^338494+36057	101897	Stefano Morozzi	03/2022
8048	2^338492+39015	101897	Stefano Morozzi	05/2022
8049	2^338494+168007	101897	Stefano Morozzi	09/2022
8050	2^338490+61149	101896	Stefano Morozzi	03/2022
8051	2^338489+161369	101896	Stefano Morozzi	04/2022
8052	2^338491+22961	101896	Stefano Morozzi	11/2022
8053	2^338487-3555	101895	Stefano Morozzi	01/2022
8054	2^338487-183129	101895	Stefano Morozzi	04/2022
8055	2^338484+128767	101894	Stefano Morozzi	01/2022
8056	2^338484-31895	101894	Stefano Morozzi	03/2022
8057	2^338483-67899	101894	Stefano Morozzi	02/2023
8058	2^338483-192129	101894	Stefano Morozzi	02/2023
8059	2^338478+10893	101893	Stefano Morozzi	03/2022
8060	2^338479+87243	101893	Stefano Morozzi	04/2022
8061	2^338479+167619	101893	Stefano Morozzi	09/2022
8062	2^338480+197503	101893	Stefano Morozzi	11/2022
8063	2^338481-11421	101893	Stefano Morozzi	12/2022
8064	2^338479-89649	101893	Stefano Morozzi	01/2023
8065	(29*34^66532-12833)/33	101893	Eric Chen	03/2023
8068	2^338475+54615	101892	Lelio R Paula	10/2016
8066	2^338475-59775	101892	Stefano Morozzi	04/2022
8067	2^338476-134237	101892	Stefano Morozzi	04/2022
8069	2^338474+100767	101891	Stefano Morozzi	11/2021
8070	2^338474+81165	101891	Stefano Morozzi	01/2022
8071	2^338474+41137	101891	Stefano Morozzi	06/2022
8072	2^338472-110445	101891	Stefano Morozzi	06/2022
8073	2^338473-89535	101891	Stefano Morozzi	01/2023
8074	2^338470+27777	101890	Stefano Morozzi	01/2022
8075	2^338468+31351	101890	Stefano Morozzi	01/2022
8076	2^338469-106339	101890	Stefano Morozzi	03/2022
8077	2^338471+187469	101890	Stefano Morozzi	04/2022
8078	2^338468+96613	101890	Stefano Morozzi	11/2022
8079	2^338469+46167	101890	Stefano Morozzi	11/2022
8080	2^338470+71527	101890	Stefano Morozzi	11/2022
8081	2^338469-112783	101890	Stefano Morozzi	12/2022
8082	2^338470-115665	101890	Stefano Morozzi	01/2023
8083	2^338467-25665	101889	Stefano Morozzi	12/2021
8084	2^338465+152139	101889	Stefano Morozzi	12/2021
8085	2^338466-28643	101889	Stefano Morozzi	01/2022
8086	2^338465+181517	101889	Stefano Morozzi	01/2022
8087	2^338466+115917	101889	Stefano Morozzi	06/2022
8088	2^338465-88291	101889	Stefano Morozzi	12/2022
8089	2^338464-104009	101888	Stefano Morozzi	02/2022
8090	2^338463+185169	101888	Stefano Morozzi	03/2022
8091	2^338464+60595	101888	Stefano Morozzi	03/2022
8092	2^338464-66377	101888	Stefano Morozzi	01/2023
8093	2^338458+60273	101887	Stefano Morozzi	03/2022
8094	2^338461+135867	101887	Stefano Morozzi	03/2022
8095	2^338455-4621	101886	Stefano Morozzi	02/2022
8096	2^338457+187827	101886	Stefano Morozzi	04/2022
8097	2^338455+173349	101886	Stefano Morozzi	11/2022
8098	2^338454+133737	101885	Stefano Morozzi	03/2022
8099	2^338454-158501	101885	Stefano Morozzi	04/2022
8100	2^338454-184217	101885	Stefano Morozzi	04/2022
8101	2^338453+164451	101885	Stefano Morozzi	05/2022
8102	2^338452-136137	101885	Stefano Morozzi	12/2022
8103	2^338450+106275	101884	Stefano Morozzi	01/2022
8104	2^338450+168439	101884	Stefano Morozzi	09/2022
8105	(133*10^101881+17)/3	101883	Robert Price	11/2021
8106	2^338445-80461	101883	Stefano Morozzi	02/2022
8107	2^338446-131211	101883	Stefano Morozzi	02/2022
8108	2^338448+187167	101883	Stefano Morozzi	04/2022
8109	2^338446-160115	101883	Stefano Morozzi	06/2022
8110	2^338447-164157	101883	Stefano Morozzi	01/2023
8111	2^338447-191001	101883	Stefano Morozzi	01/2023
8112	2^338444+127623	101882	Stefano Morozzi	12/2021
8113	2^338443-113827	101882	Stefano Morozzi	12/2022
8114	2^338441-5893	101881	Stefano Morozzi	02/2022
8115	2^338439-162565	101881	Stefano Morozzi	12/2022
8116	2^338436+153657	101880	Stefano Morozzi	01/2022
8117	2^338437-153159	101880	Stefano Morozzi	01/2022
8118	2^338436-83783	101880	Stefano Morozzi	04/2022
8119	2^338435+89109	101880	Stefano Morozzi	05/2022
8120	2^338435+13871	101880	Stefano Morozzi	05/2022
8121	2^338436+149691	101880	Stefano Morozzi	02/2023
8122	2^338434+81537	101879	Stefano Morozzi	01/2022
8123	2^338432+33495	101879	Stefano Morozzi	03/2022
8124	2^338432-7043	101879	Stefano Morozzi	03/2022
8125	2^338433-32629	101879	Stefano Morozzi	03/2022
8126	2^338430-9903	101878	Stefano Morozzi	04/2022
8134	2^338426-19797	101877	Enzo Doria	06/2013
8127	2^338427-77797	101877	Stefano Morozzi	01/2022
8128	2^338427-178687	101877	Stefano Morozzi	01/2022
8129	2^338428-54873	101877	Stefano Morozzi	02/2022
8130	2^338425+41357	101877	Stefano Morozzi	06/2022
8131	2^338428+90855	101877	Stefano Morozzi	06/2022
8132	2^338428-39807	101877	Stefano Morozzi	01/2023
8133	2^338425-192381	101877	Stefano Morozzi	02/2023
8135	2^338422-188787	101876	Stefano Morozzi	12/2022
8136	2^338423-187755	101876	Stefano Morozzi	12/2022
8137	2^338422-115865	101876	Stefano Morozzi	01/2023
8138	2^338420-178829	101875	Stefano Morozzi	01/2022
8139	2^338421-105423	101875	Stefano Morozzi	02/2022
8140	2^338419-82761	101875	Stefano Morozzi	03/2022
8141	2^338420+193143	101875	Stefano Morozzi	09/2022
8142	2^338419+199641	101875	Stefano Morozzi	02/2023
8143	2^338420-143103	101875	Stefano Morozzi	02/2023
8144	2^338418-50903	101874	Stefano Morozzi	12/2021
8145	2^338418+158355	101874	Stefano Morozzi	02/2022
8146	2^338418+159339	101874	Stefano Morozzi	03/2022
8147	2^338416+14953	101874	Stefano Morozzi	05/2022
8148	2^338416+166051	101874	Stefano Morozzi	06/2022
8149	2^338418-138765	101874	Stefano Morozzi	12/2022
8150	2^338417+49737	101874	Stefano Morozzi	02/2023
8151	2^338413-125919	101873	Stefano Morozzi	12/2021
8152	2^338414+26083	101873	Stefano Morozzi	12/2021
8153	2^338412-152379	101873	Stefano Morozzi	12/2021
8154	2^338413+54797	101873	Stefano Morozzi	01/2022
8155	2^338412+157951	101873	Stefano Morozzi	02/2022
8156	2^338414+81627	101873	Stefano Morozzi	02/2022
8157	2^338413+133679	101873	Stefano Morozzi	03/2022
8158	2^338413+197735	101873	Stefano Morozzi	11/2022
8159	2^338413-114301	101873	Stefano Morozzi	01/2023
8160	11*32^67682+395	101873	Eric Chen	04/2023
8161	2^338409-52183	101872	Stefano Morozzi	12/2021
8162	2^338411-3789	101872	Stefano Morozzi	01/2022
8163	2^338409+173237	101872	Stefano Morozzi	11/2022
8164	2^338406-184175	101871	Stefano Morozzi	04/2022
8165	2^338405+94451	101871	Stefano Morozzi	09/2022
8166	2^338406-161217	101871	Stefano Morozzi	12/2022
8167	2^338406+199929	101871	Stefano Morozzi	02/2023
8168	2^338404+55717	101870	Stefano Morozzi	01/2022
8169	2^338403+36261	101870	Stefano Morozzi	04/2022
8170	2^338402-34431	101870	Stefano Morozzi	04/2022
8171	2^338404-159215	101870	Stefano Morozzi	04/2022
8172	2^338403+18363	101870	Stefano Morozzi	09/2022
8173	2^338403+170235	101870	Stefano Morozzi	11/2022
8174	2^338399+23045	101869	Stefano Morozzi	11/2022
8175	2^338399-65535	101869	Stefano Morozzi	01/2023
8176	2^338395-127449	101868	Stefano Morozzi	12/2021
8177	2^338398-127637	101868	Stefano Morozzi	01/2022
8178	2^338398-166533	101868	Stefano Morozzi	01/2023
8179	2^338394+100317	101867	Stefano Morozzi	11/2021
8180	2^338393-152749	101867	Stefano Morozzi	01/2022
8181	2^338393+163025	101867	Stefano Morozzi	04/2022
8182	2^338393+89229	101867	Stefano Morozzi	05/2022
8183	2^338393+99647	101867	Stefano Morozzi	02/2023
8184	2^338394-192471	101867	Stefano Morozzi	02/2023
8185	2^338390+76627	101866	Stefano Morozzi	12/2021
8186	2^338389-85081	101866	Stefano Morozzi	06/2022
8187	2^338390+148113	101866	Stefano Morozzi	11/2022
8188	2^338389-14253	101866	Stefano Morozzi	01/2023
8189	2^338390-114297	101866	Stefano Morozzi	01/2023
8190	2^338391-64225	101866	Stefano Morozzi	01/2023
8191	2^338389-16971	101866	Stefano Morozzi	02/2023
8192	2^338387-75685	101865	Stefano Morozzi	12/2021
8193	2^338388-53459	101865	Stefano Morozzi	01/2022
8194	2^338388-36575	101865	Stefano Morozzi	12/2022
8195	2^338385-190311	101865	Stefano Morozzi	01/2023
8196	2^338384+131563	101864	Stefano Morozzi	01/2022
8197	2^338382+109069	101864	Stefano Morozzi	03/2022
8198	2^338384+168987	101864	Stefano Morozzi	09/2022
8199	2^338383-42367	101864	Stefano Morozzi	02/2023
8200	2^338380+77125	101863	Stefano Morozzi	12/2021
8201	2^338381-35539	101863	Stefano Morozzi	06/2022
8202	2^338378-125841	101862	Stefano Morozzi	12/2021
8203	2^338375+27815	101862	Stefano Morozzi	01/2022
8204	2^338375-28509	101862	Stefano Morozzi	01/2022
8205	2^338375+29985	101862	Stefano Morozzi	01/2022
8206	2^338377+157881	101862	Stefano Morozzi	02/2022
8207	2^338375+59589	101862	Stefano Morozzi	03/2022
8208	2^338378+36399	101862	Stefano Morozzi	04/2022
8209	2^338378-159773	101862	Stefano Morozzi	04/2022
8210	2^338378+14883	101862	Stefano Morozzi	05/2022
8211	2^338376+140173	101862	Stefano Morozzi	06/2022
8212	2^338375+18761	101862	Stefano Morozzi	09/2022
8213	2^338373-75103	101861	Stefano Morozzi	12/2021
8214	2^338372+128877	101861	Stefano Morozzi	01/2022
8215	2^338374-28731	101861	Stefano Morozzi	01/2022
8216	2^338374-128427	101861	Stefano Morozzi	01/2022
8217	2^338372+37875	101861	Stefano Morozzi	04/2022
8218	2^338373+161541	101861	Stefano Morozzi	04/2022
8219	2^338374+37759	101861	Stefano Morozzi	04/2022
8220	2^338372+93235	101861	Stefano Morozzi	09/2022
8221	2^338373-63273	101861	Stefano Morozzi	12/2022
8222	2^338369+29427	101860	Stefano Morozzi	01/2022
8223	2^338370+179133	101860	Stefano Morozzi	01/2022
8224	2^338369+131501	101860	Stefano Morozzi	01/2022
8225	2^338369+181649	101860	Stefano Morozzi	02/2022
8226	2^338370-4787	101860	Stefano Morozzi	02/2022
8227	2^338371-133491	101860	Stefano Morozzi	04/2022
8228	2^338371+42023	101860	Stefano Morozzi	09/2022
8229	2^338371+145323	101860	Stefano Morozzi	11/2022
8230	2^338371-138145	101860	Stefano Morozzi	12/2022
8237	2^338368-20369	101859	Enzo Doria	06/2013
8238	2^338366+74179	101859	Enzo Doria	04/2016
8231	2^338366+53853	101859	Stefano Morozzi	01/2022
8232	2^338365-31665	101859	Stefano Morozzi	03/2022
8233	2^338368-156345	101859	Stefano Morozzi	03/2022
8234	2^338366-159867	101859	Stefano Morozzi	04/2022
8235	2^338368-63509	101859	Stefano Morozzi	12/2022
8236	2^338365-190975	101859	Stefano Morozzi	01/2023
8239	2^338362-180845	101858	Stefano Morozzi	02/2022
8240	2^338364-155769	101858	Stefano Morozzi	02/2022
8241	2^338362+142843	101858	Stefano Morozzi	09/2022
8242	2^338362+170019	101858	Stefano Morozzi	11/2022
8243	2^338361-100875	101857	Stefano Morozzi	12/2021
8244	2^338361+154169	101857	Stefano Morozzi	01/2022
8245	2^338359-189645	101857	Stefano Morozzi	01/2023
8246	2^338356+101271	101856	Stefano Morozzi	12/2021
8247	2^338356+53383	101856	Stefano Morozzi	01/2022
8248	2^338355+59393	101856	Stefano Morozzi	03/2022
8249	2^338356+60775	101856	Stefano Morozzi	03/2022
8250	2^338356-106257	101856	Stefano Morozzi	03/2022

Find by discoverer :

PRP Records

Probable Primes Top 10000

(295107 PRPs in the top)